http://www.tripadvisor.com/ShowTopic-g190454-i147-k7123015-Stopover_in_Vienna-Vienna.html
Vienna’s City Center is very compact and less than 30 minutes away from the airport.
So, less than 1½ hrs. after landing you could be already in the City. – Assuming that you want to be at the airport another 1½ hrs. before your flight is leaving defines your time to spend in town.
With 5hrs or more to spend you are in.
First of all make sure that your passport/visa entitles you to free movement within “Schengen-Europe”. For some intercontinental connections additional security procedures could be time consuming. On the other hand, inner-European flights are processed fast.
Vienna Airport is rather small (just 3 terminals under one roof).
All means of transport to the city leave every half hour.
Although the rail service by CAT is the fastest (16 min.; and most expensive, Euro 17 RT) it does not bring you anywhere interesting on your mission.
The commuter rail (S-Bahn, 30 min.; Euro 8,80 RT) is the cheapest way it does not bring you to the center either. BUT you could go to Praterstern stop and say hallo to the Ferris Wheel!
I suggest one of the Airport Bus Lines going to “MORZINPLATZ/Schwedenplatz” (25 min.; Euro 13 RT). This brings you within 8 min. walking from St. Stephens Cathedral. The old Jewish neighborhood, now called “Bermuda Triangle” is even closer and features - since 2015 - a “Hard Rock Café” – badly needed in the city of Mozart and Beethoven.
To see the iconic Hofburg Palace and some of the monumental buildings (Parliament, City Hall etc.) of the Ring Boulevard you should have 2 hours to invest.
Make a Private Local Guide (e.g. listed with tripadvisor) meet you at the bus at “Morzinplatz” and bring you there again (if needed). A 2 hrs. walk makes sense although for the same money the guide should be available for 3 hrs. too.
For a longer stopover you could ask for more inner city walk (although 3 hrs. is enough) or make the guide meet you at the airport or even make a car/van & guide meet you at the airport and take you around in Vienna to see Belvedere and/or Schoenbrunn palaces too.
For YOUR long stopover you even could get the guide to give you 2 tours using public transportation and show you “all” or most: without burning too much money.